The sum of two angles is $83^\circ$. Angle 2 is $137^\circ$ smaller than $4$ times angle 1. What are the measures of the two angles in degrees?
Explanation: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 83}$ ${y = 4x-137}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${4x-137}$ for $y$ in the first equation. ${x + }{(4x-137)}{= 83}$ Simplify and solve for $x$ $ x+4x - 137 = 83 $ $ 5x-137 = 83 $ $ 5x = 220 $ $ x = \dfrac{220}{5} $ ${x = 44}$ Now that you know ${x = 44}$ , plug it back into $ {y = 4x-137}$ to find $y$ ${y = 4}{(44)}{ - 137}$ $y = 176 - 137$ ${y = 39}$ You can also plug ${x = 44}$ into $ {x+y = 83}$ and get the same answer for $y$ ${(44)}{ + y = 83}$ ${y = 39}$ The measure of angle 1 is $44^\circ$ and the measure of angle 2 is $39^\circ$.